Prym varieties of triple cyclic covers
Prym varieties associated to unramified triple cyclic covers are studied. We construct the Prym map from the moduli space of curves of genus \(g\) with such a cover to a certain moduli space of abelian varieties of dimension 2g-2 with a non-principal polarization and with an automorphism of order three. The main theorem is that for \(g=4\) this Prym map is generically finite of degree \(16;\) moreover, the general fiber carries a \((16_ 6)\) Kummer structure.
scientific article; zbMATH DE number 4021341
scientific article